Multiply the following complex numbers: $({-1+3i}) \cdot ({-3-5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1+3i}) \cdot ({-3-5i}) = $ $ ({-1} \cdot {-3}) + ({-1} \cdot {-5}i) + ({3}i \cdot {-3}) + ({3}i \cdot {-5}i) $ Then simplify the terms: $ (3) + (5i) + (-9i) + (-15 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 3 + (5 - 9)i - 15i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 3 + (5 - 9)i - (-15) $ The result is simplified: $ (3 + 15) + (-4i) = 18-4i $